Eric J. Fimbel - Research results and data sets - home page    back to tower of London


Problem Space of the Tower of London

Average number of steps from a configuration



Each cell is the number of steps of  a random broad-first exploration algorithm with bounded memory averaged over tasks starting from a given configuration and 2048 repetitions.

row = initial configuration; column = distance

grey: identical to lines 11..16 (same physical configurations)

  0 1 2 3 4 5 6 7 8
11 1.00 2.00 6.67 21.00 63.60 205.75 651.86 2070.80 5916.33
12 1.00 2.33 9.00 28.17 92.75 294.00 917.86 2945.25 6542.00
13 1.00 3.00 11.00 35.17 110.50 346.17 1137.00 3597.40 7971.00
14 1.00 2.33 9.00 28.50 91.33 283.00 900.25 2899.40 6818.00
15 1.00 3.00 11.00 32.75 106.60 327.40 1064.75 3371.50 7282.00
16 1.00 2.00 7.00 20.25 65.40 201.00 641.50 2025.25 5089.67
21 1.00 2.00 6.33 21.00 63.40 204.75 652.14 2073.00 5873.67
22 1.00 2.67 9.00 28.33 93.25 293.40 919.29 2941.75 6542.00
23 1.00 3.00 11.00 34.67 111.25 347.50 1138.20 3613.20 7970.00
24 1.00 2.33 9.00 28.33 91.17 281.00 898.00 2908.60 6779.00
25 1.00 3.00 11.00 32.25 107.40 327.60 1057.25 3381.50 7276.00
26 1.00 2.00 6.60 20.25 65.80 200.75 636.25 2031.00 5101.33
31 1.00 2.00 7.00 21.00 63.00 204.75 652.29 2081.40 5916.67
32 1.00 2.33 9.00 28.17 93.00 292.80 920.29 2944.75 6549.00
33 1.00 3.00 11.00 35.00 111.00 345.50 1130.00 3599.80 7999.00
34 1.00 2.33 9.00 28.50 91.00 283.00 896.25 2890.20 6776.50
35 1.00 3.00 11.00 32.50 108.00 327.20 1062.00 3376.17 7271.00
36 1.00 2.00 6.40 20.25 65.20 200.25 640.25 2031.00 5156.67
41 1.00 2.00 6.67 21.00 63.60 204.50 652.86 2078.00 5902.67
42 1.00 2.33 9.00 28.33 93.00 293.40 916.71 2938.75 6597.00
43 1.00 3.00 11.00 35.17 110.75 347.83 1130.20 3596.80 7996.00
44 1.00 2.33 9.00 28.33 90.83 282.50 900.75 2913.00 6817.50
45 1.00 3.00 11.00 32.25 106.60 327.40 1061.25 3371.17 7262.00
46 1.00 2.00 6.80 20.38 65.60 201.75 641.75 2032.50 5126.33
51 1.00 2.00 6.33 21.00 63.20 204.50 652.00 2067.20 5888.67
52 1.00 2.67 9.00 28.33 92.50 292.80 919.00 2929.00 6567.00
53 1.00 3.00 11.00 35.17 111.00 344.50 1140.20 3602.40 7949.00
54 1.00 2.67 9.00 28.50 91.17 283.25 903.50 2900.80 6779.00
55 1.00 3.00 11.00 32.50 107.60 326.60 1063.75 3379.00 7258.00
56 1.00 2.00 6.20 20.25 65.40 201.50 636.75 2039.00 5110.67
61 1.00 2.00 6.67 21.00 63.60 203.00 654.86 2081.80 5932.00
62 1.00 2.33 9.00 28.33 93.25 292.60 918.29 2942.00 6565.00
63 1.00 3.00 11.00 35.00 111.00 345.83 1136.40 3573.60 7984.00
64 1.00 2.33 9.00 28.50 91.17 281.75 894.50 2907.40 6820.00
65 1.00 3.00 11.00 32.25 107.40 326.20 1060.25 3357.50 7270.00
66 1.00 2.00 6.60 20.25 65.40 201.25 640.75 2032.50 5118.33







Copyright: (c) 2009 E.J. Fimbel, S. Lauzon, C. Rainville. This is open-access content distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.